1 Overview and introduction

1.1 Historical overview of Bose superfluids

1.2 Summary of chapters

2 Condensate dynamics at T=0

2.1 Gross-Pitaevskii（GP）equation

2.2 Bogoliubov equations for condensate fluctuations

3 Coupled equations for the condensate and thermal cloud

3.1 Generafized GP equation for the condensate

3.2 Boltzmann equation for the noncondensate atoms

3.3 Solutions in thermal equilibrium

3.4 Region of validity of the ZNG equations

4 Green's functions and self-energy approximations

4.1 Overview of Green's function approach

4.2 Nonequilibrium Green's functions in normal systems

4.3 Green's functions in a Bose-condensed gas

4.4 Classification of self-energy approximations

4.5 Dielectric formalism

5 The Beliaev and the time-dependent HFB approximations

5.1 Hartree-Fock-Bogoliubov self-energies

5.2 Beliaev self-energy approximation

5.3 Beliaev as time-dependent HFB

5.4 Density response in the Beliaev-Popov approximation

6 Kadanoff-Baym derivation of the ZNG equations

6.1 Kadanoff-Baym formalism for Bose superfluids

6.2 Hartree-Fock-Bogoliubov equations

6.3 Derivation of a kinetic equation with collisions

6.4 Collision integrals in the Hartree-Fock approximation

6.5 Generalized GP equation

6.6 Linearized collision integrals in collisionless theories

7 Kinetic equation for Bogoliubov thermal excitations

7.1 Generalized kinetic equation

7.2 Kinetic equation in the Bogoliubov-Popov approximation

7.3 Comments on improved theory

8 Static thermal cloud approximation

8.1 Condensate collective modes at finite temperatures

8.2 Phenomenological GP equations with dissipation

8.3 Relation to Pitaevskii's theory of superfluid relaxation

9 Vortices and vortex lattices at finite temperatures

9.1 Rotating frames of reference：classical treatment

9.2 Rotating frames of reference：quantum treatment

9.3 Transformation of the kinetic equation

9.4 Zaremba-Nikuni-Griffin equations in a rotating frame

9.5 Stationary states

9.6 Stationary vortex states at zero temperature

9.7 Equilibrium vortex state at finite temperatures

9.8 Nonequilibrium vortex states

10 Dynamics at finite temperatures using the moment method

10.1 Bose gas above TBEC

10.2 Scissors oscillations in a two-component superfiuid

10.3 The moment of inertia and superfluid response

11 Numerical simulation of the ZNG equations

11.1 The generalized Gross-Pitaevskii equation

11.2 Collisionless particle evolution

11.3 Collisions

11.4 Self-consistent equilibrium properties

11.5 Equilibrium collision rates

12 Simulation of collective modes at finite temperature

12.1 Equilibration

12.2 Dipole oscillations

12.3 Radial breathing mode

12.4 Scissors mode oscillations

12.5 Quadrupole collective modes

12.6 Transverse breathing mode

13 Landau damping in trapped Bose-condensed gases

13.1 Landau damping in a uniform Bose gas

13.2 Landau damping in a trapped Bose gas

13.3 Numerical results for Landau damping

14 Landau's theory of superfluidity

14.1 History of two-fluid equations

14.2 First and second sound

14.3 Dynamic structure factor in the two-fluid region

15 Two-fluid hydrodynamics in a dilute Bose gas

15.1 Equations of motion for local equilibrium

15.2 Equivalence to the Landau two-fluid equations

15.3 First and second sound in a Bose-condensed gas

15.4 Hydrodynamic modes in a trapped normal Bose gas

16 Variational formulation of the Landau two-fluid equations

16.1 Zilsel's variational formulation

16.2 The action integral for two-fluid hydrodynamics

16.3 Hydrodynamic modes in a trapped gas

16.4 Two-fluid modes in the BCS-BEC crossover at unitarity

17 The Landau-Khalatnikov two-fluid equations

17.1 The Chapman-Enskog solution of the kinetic equation

17.2 Deviation from local equilibrium

17.3 Equivalence to Landau-Khalatnikov two-fluid equations

17.4 The C12 collisions and the second viscosity coefficients

18 Transport coefficients and relaxation times

18.1 Transport coefficients in trapped Bose gases

18.2 Relaxation times for the approach to local equilibrium

18.3 Kinetic equations versus Kubo formulas

19 General theory of damping of hydrodynamic modes

19.1 Review of coupled equations for hydrodynamic modes

19.2 Normal mode frequencies

19.3 General expression for damping of hydrodynamic modes

19.4 Hydrodynamic damping in a normal Bose gas

19.5 Hydrodynamic damping in a superfluid Bose gas

Appendix A Monte Carlo calculation of collision rates

Appendix B Evaluation of transport coefficients：technical details

Appendix C Frequency-dependent transport coefficients

Appendix D Derivation of hydrodynamic damping formula

References

Index